Background

This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. biomass relationships. We use the mass balance biomass growth method for the plot biomass growth (\(G\)) calculation (briefly, plot biomass growth is a function of the change in plot biomass plus any losses due to mortality or harvest over time: \(G_{MB} = (\Delta B + M_t + C_t) / REMPER\), where \(\Delta B\) is change in plot biomass over a census interval ( \(\Delta B = B_{t + \Delta g} - B_t\) ), and \(M_t\) and \(C_t\) is the biomass of trees that died or were harvested, respectively, between two plot measurements. note: \(REMPER\) is time between two plot measurement invetvals (FIA re-measurment period). For additional details see supplementary methods. Models are fitted separately by US ecoprovince.

Hypothetically, the entire functional form of the following Michaelis-Menten non-linear model is considered: \(G = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(B_{t1}\) is the plot biomass at the first of two FIA plot tree censuses, and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(tau\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.

Data have increasing variance in \(G\) with increasing \(B\), thus, weighted nls is the best approach. We explored a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {mean B_{t1}}\) in equal-sample sized plot biomass bins (n=20 where possible, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.

Model selection is used to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine if including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest) is warranted:

model 1: simple tau model \(G = (1 + (yr-1990)* \tau/100) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

model 2: tau-alpha model \(G = (1 + (yr-1990)* \tau/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

Then, a second model selection is done using best-fitting model from part 1 and then considering additional \(p\) and \(s\) parameters (individually, and then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.

sub-model a: p form \(pA + \left( \frac {(1-p)A \cdot B_{t1}} {k+B_{t1}} \right)\)

sub model b: s form \(\left( \frac {A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)

sub model c: p and s together \(pA + \left( \frac {(1-p)A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)

NOTE:

This document contains all \(G\) observations that meet our plot-based filtering criteria:

  1. exclude FIA plots in plantation forests
  2. exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
  3. exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
  4. exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
  5. exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
  6. exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile thresholding approach. We also calculated plot \(G_{TI}\) using as summed tree incremental growth for all trees > 12.5 cm (5 inches) (see supplementary methods). We use the difference between the two methods, which we define \(diff_G\) as the difference between the two methods \(G_{MB} - G_{TI}\) to identify erroneous or outlier growth calculations. We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):

  • case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)

  • case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)

  • case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)

  • case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)

These data set cleaning criteria resulted in the exclusion of 1760 observations.

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   6822     6736.7                          
## 2   6821     7534.1  1 -797.33 -721.87      1
##   model      AIC
## 1     1 27051.87
## 2     2 27817.31
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * 
##     B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## tau   0.2671     0.1775   1.505    0.132    
## A     3.2804     0.1160  28.291   <2e-16 ***
## k     6.7587     0.6502  10.394   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9937 on 6822 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.845e-06
##   (52 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   6822     6736.7                              
## 2   6821     6727.4  1 9.3448  9.4748 0.002091 **
## 3   6821     6726.7  0 0.0000                    
## 4   6820     6726.7  1 0.0597  0.0605 0.805680   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 27051.87
## 2    1a 27044.40
## 3    1b 27043.74
## 4    1c 27045.68
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (A * 
##     B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## tau  0.25633    0.17692   1.449    0.147    
## A    3.58695    0.19865  18.056  < 2e-16 ***
## k    6.67287    0.99212   6.726 1.89e-11 ***
## s    0.65608    0.09614   6.824 9.59e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9931 on 6821 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.378e-06
##   (52 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## Warning: Removed 17 rows containing missing values (`geom_point()`).
## Warning: Removed 1038 rows containing missing values (`geom_line()`).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  18911      20242                                
## 2  18910      19105  1 1137.5  1125.9 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 70366.34
## 2     2 69274.47
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.42620    0.18105   7.877 3.52e-15 ***
## alpha -0.80627    0.02203 -36.596  < 2e-16 ***
## A      2.44488    0.06875  35.560  < 2e-16 ***
## k     10.00577    0.45256  22.109  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.005 on 18910 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.666e-07
##   (3801 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  18910      19105                                 
## 2  18909      18935  1 170.352 170.122 < 2.2e-16 ***
## 3  18909      18950  0   0.000                      
## 4  18908      18933  1  17.327  17.304 3.199e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 69274.47
## 2    2a 69107.06
## 3    2b 69122.31
## 4    2c 69107.01
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.39139    0.17819   7.809 6.08e-15 ***
## alpha  0.79883    0.02187  36.521  < 2e-16 ***
## A      2.78688    0.14055  19.828  < 2e-16 ***
## k     24.81949    2.81959   8.803  < 2e-16 ***
## p      0.19009    0.03300   5.760 8.54e-09 ***
## s      0.84678    0.09699   8.731  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.001 on 18908 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.603e-06
##   (3801 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 1926 rows containing missing values (`geom_point()`).
## Warning: Removed 1031 rows containing missing values (`geom_line()`).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7266      10676                                
## 2   7265      10233  1 442.85  314.42 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 32681.15
## 2     2 32375.18
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.80333    0.12655  -6.348 2.31e-10 ***
## alpha -0.75378    0.03983 -18.923  < 2e-16 ***
## A      5.20258    0.17244  30.171  < 2e-16 ***
## k     14.06087    1.58685   8.861  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.187 on 7265 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.702e-06
##   (64 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7265      10233                                
## 2   7264      10148  1 84.098  60.195 9.767e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 32375.18
## 2    2a 32317.19
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.86646    0.12260  -7.067 1.73e-12 ***
## alpha   0.74899    0.03917  19.122  < 2e-16 ***
## A       7.52676    0.76898   9.788  < 2e-16 ***
## k     202.76459   69.18211   2.931  0.00339 ** 
## p       0.38169    0.02784  13.708  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.182 on 7264 degrees of freedom
## 
## Number of iterations to convergence: 17 
## Achieved convergence tolerance: 9.007e-06
##   (64 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 32 rows containing missing values (`geom_point()`).
## Warning: Removed 1036 rows containing missing values (`geom_line()`).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4839     6092.2                                
## 2   4838     5805.1  1 287.09  239.26 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 20152.37
## 2     2 19920.64
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.11848    0.23118   0.512    0.608    
## alpha -0.77706    0.04598 -16.900   <2e-16 ***
## A      4.21858    0.19827  21.277   <2e-16 ***
## k     18.54761    1.56451  11.855   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.095 on 4838 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 3.671e-06
##   (1003 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_222,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4838     5805.1                                
## 2   4837     5690.5  1 114.64  97.441 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 19920.64
## 2    2a 19826.07
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.01938    0.22049   0.088     0.93    
## alpha   0.75820    0.04557  16.637  < 2e-16 ***
## A       6.20355    0.50936  12.179  < 2e-16 ***
## k     129.93261   26.49360   4.904 9.68e-07 ***
## p       0.24892    0.01539  16.178  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.085 on 4837 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 4.186e-06
##   (1003 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 489 rows containing missing values (`geom_point()`).
## Warning: Removed 1053 rows containing missing values (`geom_line()`).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8742      11815                                
## 2   8741      11535  1 280.04  212.21 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 36909.11
## 2     2 36701.34
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.77933    0.11789  -6.611 4.05e-11 ***
## alpha -0.66734    0.04291 -15.550  < 2e-16 ***
## A      4.87070    0.16409  29.683  < 2e-16 ***
## k     27.85094    2.46399  11.303  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.149 on 8741 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 7.35e-06
##   (1265 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223,  : 
##   singular gradient
##   model      AIC
## 1     2 36701.34
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.77933    0.11789  -6.611 4.05e-11 ***
## alpha -0.66734    0.04291 -15.550  < 2e-16 ***
## A      4.87070    0.16409  29.683  < 2e-16 ***
## k     27.85094    2.46399  11.303  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.149 on 8741 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 7.35e-06
##   (1265 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 620 rows containing missing values (`geom_point()`).
## Warning: Removed 1002 rows containing missing values (`geom_line()`).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13233      32413                                
## 2  13232      29231  1 3182.2  1440.5 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 69085.33
## 2     2 67719.56
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.14896    0.16799   6.839 8.30e-12 ***
## alpha -0.86934    0.02066 -42.070  < 2e-16 ***
## A      4.23734    0.11547  36.696  < 2e-16 ***
## k      1.13765    0.15945   7.135 1.02e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.486 on 13232 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.899e-06
##   (281 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13232      29231                                
## 2  13231      29135  1 96.228    43.7 3.974e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 67719.56
## 2    2a 67677.92
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.09703    0.16521   6.640 3.25e-11 ***
## alpha  0.86928    0.02053  42.333  < 2e-16 ***
## A      4.39923    0.12578  34.975  < 2e-16 ***
## k      7.58697    2.23586   3.393 0.000693 ***
## p      0.53014    0.05089  10.418  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.484 on 13231 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.544e-06
##   (281 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 143 rows containing missing values (`geom_point()`).
## Warning: Removed 1017 rows containing missing values (`geom_line()`).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13303      36087                                
## 2  13302      32461  1 3626.1  1485.9 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 69162.02
## 2     2 67754.96
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.83918    0.16820   4.989 6.14e-07 ***
## alpha -0.87045    0.02001 -43.494  < 2e-16 ***
## A      4.38516    0.13112  33.445  < 2e-16 ***
## k      5.25719    0.41118  12.786  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.562 on 13302 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 9.137e-06
##   (323 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  13302      32461                                 
## 2  13301      32152  1 309.141 127.890 < 2.2e-16 ***
## 3  13301      32176  0   0.000                      
## 4  13300      32151  1  24.408  10.097  0.001489 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 67754.96
## 2    2a 67629.63
## 3    2b 67639.59
## 4    2c 67631.50
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.75079    0.16223   4.628 3.73e-06 ***
## alpha  0.86565    0.01986  43.588  < 2e-16 ***
## A      4.83596    0.15995  30.235  < 2e-16 ***
## k     24.89028    3.99190   6.235 4.65e-10 ***
## p      0.39867    0.02422  16.458  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.555 on 13301 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.41e-06
##   (323 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 169 rows containing missing values (`geom_point()`).
## Warning: Removed 931 rows containing missing values (`geom_line()`).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1324     3607.2                                
## 2   1323     3408.5  1 198.66  77.107 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6965.867
## 2     2 6892.697
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.17879    0.83388   1.414  0.15771    
## alpha -0.80260    0.08227  -9.756  < 2e-16 ***
## A      3.93904    0.56558   6.965 5.17e-12 ***
## k      4.16920    1.51020   2.761  0.00585 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.605 on 1323 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.236e-06
##   (61 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_234,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_234,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     2 6892.697
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.17879    0.83388   1.414  0.15771    
## alpha -0.80260    0.08227  -9.756  < 2e-16 ***
## A      3.93904    0.56558   6.965 5.17e-12 ***
## k      4.16920    1.51020   2.761  0.00585 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.605 on 1323 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.236e-06
##   (61 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91861, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.1726, p-value = 3.011e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 27 rows containing missing values (`geom_point()`).
## Warning: Removed 645 rows containing missing values (`geom_line()`).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1     77     126.36                            
## 2     76     117.18  1 9.1869  5.9586 0.01697 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 417.9807
## 2     2 413.9423
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau    -0.5590     2.0350  -0.275  0.78429   
## alpha  -0.9121     0.3388  -2.692  0.00874 **
## A       9.3458     4.5294   2.063  0.04249 * 
## k      28.8091    14.7620   1.952  0.05467 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.242 on 76 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.5e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1     76     117.18                          
## 2     75     114.38  1 2.79832  1.8349 0.1796
## 3     74     114.22  1 0.15746  0.1020 0.7503
##   model      AIC
## 1     2 413.9423
## 2    2a 414.0086
## 3    2b       NA
## 4    2c 415.8984
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau    -0.5590     2.0350  -0.275  0.78429   
## alpha  -0.9121     0.3388  -2.692  0.00874 **
## A       9.3458     4.5294   2.063  0.04249 * 
## k      28.8091    14.7620   1.952  0.05467 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.242 on 76 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.5e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89128, p-value = 5.315e-06
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.28449, p-value = 0.776
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (`geom_point()`).
## Warning: Removed 725 rows containing missing values (`geom_line()`).

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   1785     2717.6                              
## 2   1784     2703.8  1 13.826  9.1224 0.002561 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7661.536
## 2     2 7654.416
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.4846     0.5115   0.947  0.34361    
## alpha  -0.3806     0.1210  -3.147  0.00168 ** 
## A       3.2219     0.3152  10.222  < 2e-16 ***
## k      15.3007     3.2666   4.684 3.03e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.231 on 1784 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 4.779e-06
##   (507 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_251,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1784     2703.8                                
## 2   1782     2593.8  2 110.03  37.797 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 7654.416
## 2    2a       NA
## 3    2b       NA
## 4    2c 7584.133
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau     0.2216     0.4513   0.491   0.6234  
## alpha   0.2054     0.1148   1.789   0.0738 .
## A       9.9611    18.2443   0.546   0.5851  
## k     350.7417   586.1704   0.598   0.5497  
## s       2.1843     1.1436   1.910   0.0563 .
## p       0.2280     0.4258   0.535   0.5924  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.206 on 1782 degrees of freedom
## 
## Number of iterations to convergence: 25 
## Achieved convergence tolerance: 8.153e-06
##   (507 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.73045, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.4834, p-value = 8.967e-11
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 254 rows containing missing values (`geom_point()`).
## Warning: Removed 1176 rows containing missing values (`geom_line()`).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    670     1600.1                          
## 2    669     1996.4  1 -396.25 -132.79      1
##   model      AIC
## 1     1 3143.502
## 2     2 3294.404
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * 
##     B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## tau  0.06116    0.86272   0.071    0.944    
## A    2.61726    0.46221   5.662 2.21e-08 ***
## k    0.65106    0.61720   1.055    0.292    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.545 on 670 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 8.46e-06
##   (44 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    670     1600.1                         
## 2    669     1598.5  1 1.5945  0.6673 0.4143
##   model      AIC
## 1     1 3143.502
## 2    1a 3144.831
## 3    1b 3144.809
## 4    1c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * 
##     B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## tau  0.06116    0.86272   0.071    0.944    
## A    2.61726    0.46221   5.662 2.21e-08 ***
## k    0.65106    0.61720   1.055    0.292    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.545 on 670 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 8.46e-06
##   (44 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91752, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.2822, p-value = 1.276e-07
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 25 rows containing missing values (`geom_point()`).
## Warning: Removed 1235 rows containing missing values (`geom_line()`).

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • note: model fit, but fit was funky due to data being sparse

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    212     109.50                              
## 2    211     105.09  1 4.4098   8.854 0.003266 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 506.5831
## 2     2 499.7454
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.4057     0.8630  -1.629 0.104840    
## alpha  -0.8581     0.2552  -3.363 0.000917 ***
## A       4.8742     1.6179   3.013 0.002906 ** 
## k     126.0935    43.2118   2.918 0.003904 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7057 on 211 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 1.9e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_313,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    211    105.089                            
## 2    210    102.361  1 2.7279  5.5964 0.01891 *
## 3    209     99.895  1 2.4666  5.1606 0.02412 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 499.7454
## 2    2a 496.0908
## 3    2b       NA
## 4    2c 492.8465
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -1.45800    0.80966  -1.801 0.073181 .  
## alpha   0.86175    0.24671   3.493 0.000583 ***
## A       3.53528    1.11165   3.180 0.001695 ** 
## k     108.86093   23.64573   4.604  7.2e-06 ***
## s       3.01534    1.38858   2.172 0.031017 *  
## p       0.31269    0.09234   3.386 0.000846 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6914 on 209 degrees of freedom
## 
## Number of iterations to convergence: 17 
## Achieved convergence tolerance: 6.641e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9805, p-value = 0.004507
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.34157, p-value = 0.7327
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (`geom_point()`).
## Warning: Removed 1103 rows containing missing values (`geom_line()`).

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Error in nls(fg_1, data = G_331, start = c(tau = tau.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_331, start = c(tau = tau.start, alpha = alpha.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)  
## 1    193     173.52                           
## 2    192     168.70  1 4.8201  5.4858 0.0202 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 665.6359
## 2     2 662.1143
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau     0.8048     1.7052   0.472  0.63747   
## alpha  -0.6583     0.2567  -2.564  0.01110 * 
## A       3.8161     1.2658   3.015  0.00292 **
## k      57.9499    19.0680   3.039  0.00270 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9374 on 192 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.683e-06
##   (36 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_332,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    192     168.70                              
## 2    191     160.56  1 8.1352  9.6773 0.002152 **
## 3    190     158.50  1 2.0692  2.4805 0.116929   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 662.1143
## 2    2a 654.4271
## 3    2b       NA
## 4    2c 653.8849
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau    0.52731    1.48372   0.355  0.72269   
## alpha  0.67320    0.22864   2.944  0.00364 **
## A      3.71061    1.25148   2.965  0.00342 **
## k     85.53537   27.33749   3.129  0.00203 **
## p      0.28897    0.09744   2.966  0.00341 **
## s      2.32866    1.15746   2.012  0.04565 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9133 on 190 degrees of freedom
## 
## Number of iterations to convergence: 14 
## Achieved convergence tolerance: 6.979e-06
##   (36 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91126, p-value = 1.852e-09
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.2715, p-value = 0.2035
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 21 rows containing missing values (`geom_point()`).
## Warning: Removed 1120 rows containing missing values (`geom_line()`).

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    112     82.270                                
## 2    111     74.205  1  8.065  12.064 0.0007339 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 315.0331
## 2     2 305.1679
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.9428     5.3488   0.363   0.7171    
## alpha  -0.9852     0.2434  -4.048 9.58e-05 ***
## A       3.2751     2.6546   1.234   0.2199    
## k      82.6440    32.5518   2.539   0.0125 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8176 on 111 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.756e-06
##   (9 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    111     74.205                          
## 2    110     74.164  1 0.04076  0.0605 0.8062
##   model      AIC
## 1     2 305.1679
## 2    2a 307.1047
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.9428     5.3488   0.363   0.7171    
## alpha  -0.9852     0.2434  -4.048 9.58e-05 ***
## A       3.2751     2.6546   1.234   0.2199    
## k      82.6440    32.5518   2.539   0.0125 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8176 on 111 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.756e-06
##   (9 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94862, p-value = 0.0002394
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.94042, p-value = 0.347
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing missing values (`geom_point()`).
## Warning: Removed 1241 rows containing missing values (`geom_line()`).

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6746     5753.1                                
## 2   6745     5409.4  1  343.7  428.55 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 25694.00
## 2     2 25280.27
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.66462    0.19759   3.364 0.000774 ***
## alpha -0.64343    0.02893 -22.243  < 2e-16 ***
## A      3.07739    0.11482  26.801  < 2e-16 ***
## k      2.85208    0.41233   6.917 5.04e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8955 on 6745 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.962e-06
##   (23 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   6745     5409.4                              
## 2   6744     5406.1  1 3.3122  4.1319 0.042121 * 
## 3   6744     5409.2  0 0.0000                    
## 4   6743     5402.0  1 7.1869  8.9709 0.002753 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 25280.27
## 2    2a 25278.13
## 3    2b 25281.98
## 4    2c 25275.01
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.65138    0.19644   3.316 0.000918 ***
## alpha  0.64104    0.02888  22.198  < 2e-16 ***
## A      3.03312    0.11388  26.634  < 2e-16 ***
## k      9.63600    2.28136   4.224 2.43e-05 ***
## p      0.44875    0.08007   5.604 2.17e-08 ***
## s      1.77709    0.43212   4.113 3.96e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8951 on 6743 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.728e-06
##   (23 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 10 rows containing missing values (`geom_point()`).
## Warning: Removed 1108 rows containing missing values (`geom_line()`).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8257      16789                                
## 2   8256      16419  1  369.5  185.79 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 40113.33
## 2     2 39931.50
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.02238    0.16479  -0.136    0.892    
## alpha -0.81544    0.05665 -14.395  < 2e-16 ***
## A      4.21394    0.15149  27.817  < 2e-16 ***
## k      7.39990    1.43242   5.166 2.45e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.41 on 8256 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 5.344e-06
##   (55 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M221,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M221,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model     AIC
## 1     2 39931.5
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.02238    0.16479  -0.136    0.892    
## alpha -0.81544    0.05665 -14.395  < 2e-16 ***
## A      4.21394    0.15149  27.817  < 2e-16 ***
## k      7.39990    1.43242   5.166 2.45e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.41 on 8256 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 5.344e-06
##   (55 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 29 rows containing missing values (`geom_point()`).
## Warning: Removed 982 rows containing missing values (`geom_line()`).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    887     1339.4                                
## 2    886     1293.6  1 45.802  31.369 2.846e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3727.581
## 2     2 3698.615
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     3.1263     1.5722   1.989   0.0471 *  
## alpha  -0.9187     0.1511  -6.082 1.77e-09 ***
## A       1.7439     0.3583   4.866 1.34e-06 ***
## k       3.5365     3.1342   1.128   0.2595    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.208 on 886 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 7.383e-06
##   (6 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    886     1293.6                          
## 2    885     1298.1  1 -4.4727 -3.0494      1
##   model      AIC
## 1     2 3698.615
## 2    2a 3703.687
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     3.1263     1.5722   1.989   0.0471 *  
## alpha  -0.9187     0.1511  -6.082 1.77e-09 ***
## A       1.7439     0.3583   4.866 1.34e-06 ***
## k       3.5365     3.1342   1.128   0.2595    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.208 on 886 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 7.383e-06
##   (6 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94608, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.0441, p-value = 0.04094
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 3 rows containing missing values (`geom_point()`).
## Warning: Removed 1175 rows containing missing values (`geom_line()`).

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    989     1487.8                                
## 2    988     1416.7  1 71.015  49.524 3.661e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4215.211
## 2     2 4168.693
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     4.9467     2.5181   1.964 0.049759 *  
## alpha  -0.7944     0.1046  -7.597    7e-14 ***
## A       1.4589     0.3868   3.772 0.000172 ***
## k       1.4613     0.9078   1.610 0.107771    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.197 on 988 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 8.21e-06
##   (14 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     2 4168.693
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     4.9467     2.5181   1.964 0.049759 *  
## alpha  -0.7944     0.1046  -7.597    7e-14 ***
## A       1.4589     0.3868   3.772 0.000172 ***
## k       1.4613     0.9078   1.610 0.107771    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.197 on 988 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 8.21e-06
##   (14 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9557, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.4105, p-value = 6.286e-08
## alternative hypothesis: two.sided

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## Warning: Removed 6 rows containing missing values (`geom_point()`).
## Warning: Removed 1218 rows containing missing values (`geom_line()`).

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3147     8417.1                                
## 2   3146     8013.0  1 404.08  158.65 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 16149.88
## 2     2 15996.91
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.7104     0.2352  -7.271 4.47e-13 ***
## alpha  -0.9679     0.0693 -13.967  < 2e-16 ***
## A      12.8005     1.0512  12.177  < 2e-16 ***
## k     128.0294    10.2047  12.546  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.596 on 3146 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.03e-06
##   (74 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   3146     8013.0                                 
## 2   3145     7895.5  1 117.522  46.813 9.349e-12 ***
## 3   3145     7927.2  0   0.000                      
## 4   3144     7884.8  1  42.386  16.901 4.038e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 15996.91
## 2    2a 15952.37
## 3    2b 15965.01
## 4    2c 15950.12
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -1.69947    0.23420  -7.256 4.98e-13 ***
## alpha   0.93948    0.06980  13.459  < 2e-16 ***
## A      11.74044    1.14133  10.287  < 2e-16 ***
## k     171.08730   20.21043   8.465  < 2e-16 ***
## p       0.20420    0.03023   6.755 1.70e-11 ***
## s       1.60173    0.23623   6.780 1.43e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.584 on 3144 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 6.004e-06
##   (74 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92456, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.5939, p-value = 4.35e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 38 rows containing missing values (`geom_point()`).
## Warning: Removed 126 rows containing missing values (`geom_line()`).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1682     3723.6                                
## 2   1681     3631.6  1 91.984  42.578 8.964e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7999.216
## 2     2 7959.068
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.7342     0.3391  -5.114 3.52e-07 ***
## alpha  -0.7483     0.1059  -7.063 2.37e-12 ***
## A      15.7046     1.8786   8.360  < 2e-16 ***
## k     237.0276    28.7807   8.236 3.55e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.47 on 1681 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.485e-06
##   (292 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1681     3631.6                                
## 2   1680     3599.4  1 32.142  15.002 0.0001115 ***
## 3   1680     3620.7  0  0.000                      
## 4   1679     3591.9  1 28.717  13.424 0.0002562 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 7959.068
## 2    2a 7946.088
## 3    2b 7955.994
## 4    2c 7944.576
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -1.69541    0.34600  -4.900 1.05e-06 ***
## alpha   0.74116    0.10357   7.156 1.24e-12 ***
## A      13.70695    2.47143   5.546 3.39e-08 ***
## k     225.44963   53.31612   4.229 2.48e-05 ***
## p       0.10497    0.03363   3.121  0.00183 ** 
## s       1.39890    0.24458   5.720 1.26e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.463 on 1679 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.741e-06
##   (292 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89641, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.6852, p-value = 0.09195
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 154 rows containing missing values (`geom_point()`).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    363     173.85                                
## 2    362     154.17  1  19.68  46.209 4.395e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 867.4285
## 2     2 825.4588
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -2.2781     0.2890  -7.883 3.78e-14 ***
## alpha  -0.8248     0.1070  -7.706 1.26e-13 ***
## A       9.7691     1.7843   5.475 8.19e-08 ***
## k     158.4554    37.6226   4.212 3.20e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6526 on 362 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.138e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    362     154.17                          
## 2    361     153.17  1 1.00231  2.3623 0.1252
## 3    361     153.11  0 0.00000               
## 4    360     153.10  1 0.00292  0.0069 0.9341
##   model      AIC
## 1     2 825.4588
## 2    2a 825.0716
## 3    2b 824.9169
## 4    2c 826.9099
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau      -2.2633     0.2924  -7.741 1.00e-13 ***
## alpha     0.8207     0.1072   7.655 1.78e-13 ***
## A        46.4898   151.8218   0.306 0.759619    
## k      3531.0905 21347.2370   0.165 0.868712    
## s         0.6912     0.1784   3.874 0.000127 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6512 on 361 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 2.197e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97183, p-value = 1.539e-06
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 1.2648, p-value = 0.2059
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1183 rows containing missing values (`geom_line()`).

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1732     1567.7                                
## 2   1731     1472.8  1 94.836  111.46 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4946.994
## 2     2 4840.726
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.76227    0.57791  -1.319    0.187    
## alpha -0.70080    0.05633 -12.441  < 2e-16 ***
## A      2.47728    0.38500   6.434 1.60e-10 ***
## k     36.87998    6.05255   6.093 1.36e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9224 on 1731 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 4.598e-06
##   (21 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M331,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M331,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1731     1472.8                                
## 2   1730     1444.8  1 28.005  33.533 8.306e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 4840.726
## 2    2a 4809.418
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.52155    0.64055  -0.814  0.41563    
## alpha   0.71336    0.05463  13.058  < 2e-16 ***
## A       5.86779    2.73742   2.144  0.03221 *  
## k     480.19280  344.85521   1.392  0.16397    
## p       0.12897    0.04919   2.622  0.00883 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9139 on 1730 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.581e-07
##   (21 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.85285, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.0675, p-value = 1.299e-09
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 7 rows containing missing values (`geom_point()`).
## Warning: Removed 1091 rows containing missing values (`geom_line()`).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2513     2864.1                                
## 2   2512     2605.7  1 258.36  249.07 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8728.807
## 2     2 8492.947
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.83940    0.43557  -1.927   0.0541 .  
## alpha -0.90696    0.04938 -18.366  < 2e-16 ***
## A      4.67956    0.57797   8.097 8.72e-16 ***
## k     63.69769    7.00966   9.087  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.018 on 2512 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 5.412e-06
##   (96 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M332,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2512     2605.7                                
## 2   2511     2493.1  1 112.67  113.49 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 8492.947
## 2    2a 8383.730
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.90399    0.40784  -2.216  0.02675 *  
## alpha   0.88994    0.04846  18.364  < 2e-16 ***
## A      15.03808    5.94947   2.528  0.01154 *  
## k     778.59152  400.54032   1.944  0.05202 .  
## p       0.07483    0.02517   2.972  0.00298 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9964 on 2511 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 2.226e-06
##   (96 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90403, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.8038, p-value = 1.019e-11
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 54 rows containing missing values (`geom_point()`).
## Warning: Removed 1001 rows containing missing values (`geom_line()`).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1691     2122.4                                
## 2   1690     1851.2  1 271.16  247.54 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6712.211
## 2     2 6482.658
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.57735    0.57364  -1.006    0.314    
## alpha -0.94904    0.05263 -18.031  < 2e-16 ***
## A      5.53729    0.80951   6.840  1.1e-11 ***
## k     44.22062    4.89719   9.030  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.047 on 1690 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 9.13e-06
##   (59 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M333,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M333,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1690     1851.2                                
## 2   1689     1754.2  1 97.099  93.493 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 6482.658
## 2    2a 6393.391
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.64166    0.54008  -1.188 0.234968    
## alpha   0.93153    0.05060  18.408  < 2e-16 ***
## A      13.16763    3.39124   3.883 0.000107 ***
## k     464.03966  162.05800   2.863 0.004243 ** 
## p       0.11466    0.02073   5.532 3.67e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.019 on 1689 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 9.076e-06
##   (59 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93181, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.6928, p-value = 2.695e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 26 rows containing missing values (`geom_point()`).
## Warning: Removed 925 rows containing missing values (`geom_line()`).

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    355     353.04                                
## 2    354     327.07  1 25.967  28.104 2.028e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1090.416
## 2     2 1065.066
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.06351    1.23785   0.051 0.959111    
## alpha -0.80377    0.13376  -6.009 4.64e-09 ***
## A      2.35196    0.61035   3.853 0.000138 ***
## k     29.82188    9.39819   3.173 0.001640 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9612 on 354 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 9.666e-06
##   (101 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    354     327.07                          
## 2    353     327.04  1 0.03769  0.0407 0.8403
## 3    353     327.03  0 0.00000               
## 4    352     326.23  1 0.80050  0.8637 0.3533
##   model      AIC
## 1     2 1065.066
## 2    2a 1067.025
## 3    2b 1067.014
## 4    2c 1068.136
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.06351    1.23785   0.051 0.959111    
## alpha -0.80377    0.13376  -6.009 4.64e-09 ***
## A      2.35196    0.61035   3.853 0.000138 ***
## k     29.82188    9.39819   3.173 0.001640 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9612 on 354 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 9.666e-06
##   (101 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.83083, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.0095, p-value = 0.002616
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 40 rows containing missing values (`geom_point()`).
## Warning: Removed 1264 rows containing missing values (`geom_line()`).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 1b
212 Laurentian Mixed Forest 2c
221 Eastern Broadleaf Forest 2a
222 Midwest Broadleaf Forest 2a
223 Central Interior Broadleaf Forest 2
231 Southeastern Mixed Forest 2a
232 Outer Coastal Plain Mixed Forest 2a
234 Lower Mississippi Riverine Forest 2
242 Pacific Lowland Mixed Forest 2
251 Prairie Parkland (Temperate) 2c
255 Prairie Parkland (Subtropical) 1
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert 2c
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe 2c
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert 2
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2c
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2
M223 Ozark Broadleaf Forest Meadow 2
M231 Ouachita Mixed Forest 2
M242 Cascade Mixed Forest 2c
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2c
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 2b
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 2a
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2a
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2a
M334 Black Hills Coniferous Forest 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots tau tau.variance tau.2.5 tau.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5
211 Northeastern Mixed Forest east 6877 2876 0.2563300 0.0313012 -0.0904912 0.6031512 NA NA NA NA 3.586948 3.1975283 3.976368 6.6728734 4.728000e+00 8.617747
212 Laurentian Mixed Forest east 22715 9499 1.3913875 0.0317501 1.0421278 1.7406472 0.7988278 0.0004784 0.7559542 0.8417013 2.786876 2.5113784 3.062373 24.8194914 1.929284e+01 30.346147
221 Eastern Broadleaf Forest east 7333 3571 -0.8664562 0.0150309 -1.1067890 -0.6261234 0.7489933 0.0015342 0.6722112 0.8257755 7.526758 6.0193286 9.034187 202.7645861 6.714754e+01 338.381632
222 Midwest Broadleaf Forest east 5845 2589 0.0193829 0.0486172 -0.4128837 0.4516496 0.7582044 0.0020771 0.6688572 0.8475515 6.203547 5.2049709 7.202122 129.9326131 7.799312e+01 181.872103
223 Central Interior Broadleaf Forest east 10010 3864 -0.7793322 0.0138981 -1.0104251 -0.5482392 -0.6673416 0.0018417 -0.7514642 -0.5832189 4.870700 4.5490425 5.192357 27.8509429 2.302094e+01 32.680950
231 Southeastern Mixed Forest east 13517 6193 1.0970279 0.0272942 0.7731933 1.4208625 0.8692755 0.0004217 0.8290255 0.9095256 4.399229 4.1526809 4.645777 7.5869657 3.204365e+00 11.969566
232 Outer Coastal Plain Mixed Forest east 13629 6626 0.7507905 0.0263187 0.4327960 1.0687850 0.8656530 0.0003944 0.8267250 0.9045811 4.835960 4.5224431 5.149478 24.8902847 1.706559e+01 32.714974
234 Lower Mississippi Riverine Forest east 1388 778 1.1787939 0.6953602 -0.4570826 2.8146704 -0.8025954 0.0067680 -0.9639845 -0.6412062 3.939045 2.8295221 5.048568 4.1692019 1.206553e+00 7.131851
242 Pacific Lowland Mixed Forest pacific 83 83 -0.5590174 4.1412960 -4.6121059 3.4940711 -0.9120660 0.1148026 -1.5868951 -0.2372368 9.345847 0.3247658 18.366928 28.8091141 -5.919517e-01 58.210180
251 Prairie Parkland (Temperate) east 2295 906 0.2216359 0.2037144 -0.6635898 1.1068616 0.2054172 0.0131859 -0.0197979 0.4306323 9.961071 -25.8213578 45.743499 350.7416996 -7.989121e+02 1500.395489
255 Prairie Parkland (Subtropical) east 717 319 0.0611564 0.7442863 -1.6328044 1.7551171 NA NA NA NA 2.617256 1.7096987 3.524814 0.6510643 -5.608122e-01 1.862941
261 California Coastal Chaparral Forest and Shrub pacific 25 25 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 163 161 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 218 218 -1.4580008 0.6555427 -3.0541398 0.1381382 0.8617501 0.0608675 0.3753845 1.3481157 3.535280 1.3438044 5.726756 108.8609268 6.224623e+01 155.475628
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 331 255 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 232 128 0.5273135 2.2014395 -2.3993756 3.4540026 0.6732000 0.0522762 0.2222013 1.1241987 3.710606 1.2420309 6.179182 85.5353659 3.161140e+01 139.459329
341 Intermountain Semi-Desert and Desert interior west 66 64 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 124 123 1.9428128 28.6091636 -8.6560993 12.5417248 -0.9851536 0.0592234 -1.4673851 -0.5029222 3.275141 -1.9851322 8.535414 82.6440257 1.814043e+01 147.147617
411 Everglades east 96 63 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6772 3006 0.6513800 0.0385875 0.2663014 1.0364587 0.6410399 0.0008339 0.5844300 0.6976499 3.033122 2.8098797 3.256365 9.6360019 5.163818e+00 14.108185
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8315 3810 -0.0223837 0.0271568 -0.3454200 0.3006526 -0.8154360 0.0032089 -0.9264781 -0.7043938 4.213936 3.9169781 4.510893 7.3998973 4.591995e+00 10.207799
M223 Ozark Broadleaf Forest Meadow east 896 349 3.1263420 2.4716768 0.0407563 6.2119277 -0.9186634 0.0228168 -1.2151257 -0.6222011 1.743872 1.0405732 2.447170 3.5364747 -2.614832e+00 9.687782
M231 Ouachita Mixed Forest east 1006 495 4.9466961 6.3409406 0.0052133 9.8881789 -0.7943535 0.0109322 -0.9995334 -0.5891735 1.458943 0.6999145 2.217972 1.4612679 -3.200901e-01 3.242626
M242 Cascade Mixed Forest pacific 3224 3207 -1.6994737 0.0548502 -2.1586764 -1.2402711 0.9394760 0.0048721 0.8026171 1.0763350 11.740440 9.5026144 13.978265 171.0873034 1.314603e+02 210.714270
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 1977 1807 -1.6954110 0.1197185 -2.3740549 -1.0167672 0.7411577 0.0107271 0.5380143 0.9443011 13.706949 8.8595352 18.554362 225.4496302 1.208766e+02 330.022689
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 30 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 367 367 -2.2633319 0.0854902 -2.8383280 -1.6883359 0.8206775 0.0114930 0.6098518 1.0315032 46.489850 -252.0764727 345.056172 3531.0904921 -3.844947e+04 45511.650585
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 1756 1756 -0.5215501 0.4103002 -1.7778776 0.7347775 0.7133635 0.0029846 0.6062123 0.8205148 5.867793 0.4987919 11.236793 480.1928029 -1.961842e+02 1156.569814
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2612 2602 -0.9039865 0.1663372 -1.7037327 -0.1042403 0.8899359 0.0023485 0.7949068 0.9849650 15.038079 3.3717145 26.704444 778.5915153 -6.831681e+00 1564.014712
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 1753 1742 -0.6416558 0.2916837 -1.7009473 0.4176356 0.9315265 0.0025607 0.8322748 1.0307783 13.167626 6.5161470 19.819105 464.0396645 1.461840e+02 781.895283
M334 Black Hills Coniferous Forest interior west 459 181 0.0635085 1.5322693 -2.3709535 2.4979705 -0.8037708 0.0178929 -1.0668432 -0.5406984 2.351961 1.1515878 3.552334 29.8218782 1.133858e+01 48.305176
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 220 220 NA NA NA NA NA NA NA NA NA NA NA NA NA NA

parameter variance co-variance

## png 
##   2

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation ideoms with `aes()`
## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot alpha (biomass growth compensation effect)

plot A (asymptote of forest biomass growth in Mg/ha/yr)

## Warning: Removed 12 rows containing missing values (`geom_point()`).

plot k (stand biomass at half biomss G in Mg/ha)

## Warning: Removed 12 rows containing missing values (`geom_point()`).

Caclulations - weighted averages

tau (stand biomass productivity trend in % 2000-2021)

##          region weighted.tau weighted.tau.std_Error 95 % CI, upper
## 1     entire US   0.21477279             0.06490419     0.34198500
## 2       pacific  -0.14778107             0.01712126    -0.11422340
## 3          east   0.45260667             0.05268286     0.55586508
## 4 interior west  -0.09005281             0.03382207    -0.02376156
##   95 % CI, lower
## 1     0.08756058
## 2    -0.18133874
## 3     0.34934826
## 4    -0.15634406

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US     0.48701599              0.010032499     0.50667969
## 2       pacific     0.07382771              0.005060543     0.08374637
## 3          east     0.31824548              0.007951336     0.33383010
## 4 interior west     0.09494281              0.003437762     0.10168082
##   95 % CI, lower
## 1     0.46735229
## 2     0.06390905
## 3     0.30266086
## 4     0.08820479

A (asymptote of forest biomass growth in Mg/ha/yr)

##          region weighted.A
## 1     entire US   6.076233
## 2       pacific  11.962096
## 3          east   4.389088
## 4 interior west  11.887101

K (stand biomass at half biomass G in Mg/ha)

##          region weighted.k
## 1     entire US  138.06413
## 2       pacific  181.42260
## 3          east   44.83991
## 4 interior west  652.58823